S. R. Hassan

Orbital-selective Mott transition out of band degeneracy lifting.

We outline a general mechanism for orbital-selective Mott transition, the coexistence of both itinerant and localized conduction electrons, and show how it can take place in a wide range of realistic situations, even for bands of identical width and correlation, provided a crystal field splits the energy levels in manifolds with different degeneracies and the exchange coupling is large enough to reduce orbital fluctuations. The mechanism relies on the different kinetic energy in manifolds with different degeneracy. This phase has Curie-Weiss susceptibility and non-Fermi-liquid behavior, which disappear at a critical doping, all of which is reminiscent of the physics of the pnictides.

Absence of Spin Liquid in Nonfrustrated Correlated Systems

The question of the existence of a spin liquid state in the half-filled Hubbard model on the honeycomb (also known as graphene) lattice is revisited. The variational cluster approximation, the cluster dynamical mean field theory, and the cluster dynamical impurity approximation are applied to various cluster systems. Assuming that the spin liquid phase coincides with the Mott insulating phase in this nonfrustrated system, we find that the Mott transition is preempted by a magnetic transition occurring at a lower value of the interaction U, and therefore the spin liquid phase does not occur. This conclusion is obtained using clusters with two bath orbitals connected to each boundary cluster site. We argue that using a single bath orbital per boundary site is insufficient and leads to the erroneous conclusion that the system is gapped for all nonzero values of U.

Antiferromagnetism in the Hubbard model on the honeycomb lattice: a Two-Particle Self-Consistent study

The semimetal to antiferromagnet quantum phase transition of the Hubbard model on the honeycomb lattice has come to the forefront in the context of the proposal that a semimetal to spin liquid transition can occur before the transition to the antiferromagnetic phase. To study the semimetal to antiferromagnet transition, we generalize the two-particle self-consistent (TPSC) approach to the honeycomb lattice (a structure that can be realized in graphene for example). We show that the critical interaction strength where the transition occurs is

Competition between charge and spin order in the t-U-V extended Hubbard model on the triangular lattice

U_c/t=3.79\pm 0.01

Stable Algebraic Spin Liquid in a Hubbard Model

quite close to the value

Conditions for magnetically induced singlet d-wave superconductivity on the square lattice

U_c/t=3.869 \pm 0.013

Slave spins away from half filling: Cluster mean-field theory of the Hubbard and extended Hubbard models

reported using large-scale quantum Monte Carlo simulations. This reinforces the conclusion that the semimetal to spin liquid transition is pre-empted by the transition to the antiferromagnet. Since TPSC satisfies the Mermin-Wagner theorem, we find temperature-dependent results for the antiferromagnetic and ferromagnetic correlation lengths as well as the dependence of double occupancy and of the renormalized spin and charge interactions on the bare interaction strength. We also estimate the value of the crossover temperature to the renormalized classical regime as a function of interaction strength.

Quarter-filled Kitaev-Hubbard model: A quantum Hall state in an optical lattice

Several new classes of compounds can be modeled in first approximation by electrons on the triangular lattice that interact through on-site repulsion U as well as nearest-neighbor repulsion V. This extended Hubbard model on a triangular lattice has been studied mostly in the strong coupling limit for only a few types of instabilities. Using the extended two-particle self-consistent approach ETPSC, that is valid at weak to intermediate coupling, we present an unbiased study of the density and interaction dependent crossover diagram for spin- and charge-density wave instabilities of the normal state at arbitrary wave vector. When U dominates over V and electron filling is large, instabilities are chiefly in the spin sector and are controlled mostly by Fermi surface properties. Increasing V eventually leads to charge instabilities. In the latter case, it is mostly the wave vector dependence of the vertex that determines the wave vector of the instability rather than Fermi surface properties. At small filling, nontrivial instabilities appear only beyond the weak coupling limit. There again, charge-density wave instabilities are favored over a wide range of dopings by large V at wave vectors corresponding to 33 superlattice in real space. Commensurate fillings do not play a special role for this instability. Increasing U leads to competition with ferromagnetism. At negative values of U or V, neglecting superconducting fluctuations, one finds that charge instabilities are favored. In general, the crossover diagram presents a rich variety of instabilities. We also show that thermal charge-density wave fluctuations in the renormalized-classical regime can open a pseudogap in the single-particle spectral weight, just as spin or superconducting fluctuations.

Mott p-n junctions in layered materials

We show the existence of a stable algebraic spin liquid (ASL) phase in a Hubbard model defined on a honeycomb lattice with spin-dependent hopping that breaks time-reversal symmetry. The effective spin model is the Kitaev model for large on-site repulsion. The gaplessness of the emergent Majorana fermions is protected by the time-reversal invariance of this model. We prove that the effective spin model is time-reversal invariant in the entire Mott phase, thus ensuring the stability of the ASL. The model can be physically realized in cold atom systems, and we propose experimental signals of the ASL.

Supersolidity, entropy and frustration

It is expected that at weak to intermediate coupling, d-wave superconductivity can be induced by antiferromagnetic fluctuations. However, one needs to clarify the role of Fermi surface topology, density of states, pseudogap, and wave vector of the magnetic fluctuations on the nature and strength of the induced d-wave state. To this end, we study the generalized phase diagram of the two-dimensional half-filled Hubbard model as a function of interaction strength